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Independence, randomness and the axiom of choice

Published online by Cambridge University Press:  12 March 2014

Michiel van Lambalgen
Michiel van Lambalgen*
Affiliation:
Department of Mathematics, University of Amsterdam, Amsterdam, The Netherlands, E-mail: [email protected]
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Abstract

We investigate various ways of introducing axioms for randomness in set theory. The results show that these axioms, when added to ZF, imply the failure of AC. But the axiom of extensionality plays an essential role in the derivation, and a deeper analysis may ultimately show that randomness is incompatible with extensionality.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 4 , December 1992 , pp. 1274 - 1304
Copyright
Copyright © Association for Symbolic Logic 1992

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